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Semilinear relations and *-representations of deformations of so(3)

Yuriĭ SamoĭlenkoLyudmila Turowska — 1997

Banach Center Publications

We study a family of commuting selfadjoint operators = ( A k ) k = 1 n , which satisfy, together with the operators of the family = ( B j ) j = 1 n , semilinear relations i f i j ( ) B j g i j ( ) = h ( ) , ( f i j , g i j , h j : n are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra U q ' ( s o ( 3 ) ) .

Growth and smooth spectral synthesis in the Fourier algebras of Lie groups

Jean LudwigLyudmila Turowska — 2006

Studia Mathematica

Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate...

Schur and operator multipliers

Ivan G. TodorovLyudmila Turowska — 2010

Banach Center Publications

The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative case...

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